Finite Group Databasebeta

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D₃×#13025 #72258704

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

2916 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 23 points:

(2,3);(1,2,3)(9,13)(10,18)(11,19)(14,16)(15,21)(17,23)(20,22);(4,5,6,7)(10,17)(13,21)(14,22)(18,23);(8,9)(10,13)(11,20)(12,15)(14,18)(16,19)(17,21)(22,23)

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((2,3), (1,2,3)(9,13)(10,18)(11,19)(14,16)(15,21)(17,23)(20,22), (4,5,6,7)(10,17)(13,21)(14,22)(18,23), (8,9)(10,13)(11,20)(12,15)(14,18)(16,19)(17,21)(22,23));